Both Batman and Diana are smart enough to know that if you let people go around killing other people whenever they feel justified, even if it is just, it causes the complete breakdown of social order. Danny kills those guys sure; then maybe someone from their family kills Danny, and someone from Danny's family kills that guy, and it never ends. This is why an impartial justice system is necessary - and why, even if it fails, you can't just circumvent it and avoid the consequences because you thought it was just.